Obtaining a quantitative description of enzyme catalysis is one of the most fundamental problems in molecular biology. Here, we propose the continuation of our long-term research project aimed at the development improvement and validation of computational models for quantitative structure-catalysis correlation of enzyme-substrate complexes. In the previous grant periods we have developed the Empirical Valence Bond (EVB) method and combined it with Free Energy Perturbation (FEP) methods, thus providing a practical and reasonably reliable way to simulate enzymatic reactions. Further, we also explored the applicability of molecular orbital based methods, using hybrid quantum/classical strategies and performed preliminary calculations with a new ab initio pseudo-potential method. Our approaches have been used in studies of several genetically modified enzymes and analyses of various classes of enzymatic reactions, including proton and hydride transfer, and the chemistry of metallo-enzymes. Presently, we would like to continue our efforts on the following fronts: i) Extensive study of a variety of reactions that have currently received great interest. These include the mechanisms of action of aspartic proteases, e.g. HIV-1 protease, dihydrofolate reductase (DHFR), alcohol dehydrogenase (ADH) and DNA polymerases. In addition, the study of serine and cysteine proteases will be continued. ii) Development of more accurate potential surfaces for enzymatic reactions, exploration of the parameterization of EVB off-diagonal elements by ab initio methods and the development of estimation methods for the solvent effect on these off- diagonal elements using pseudo-potential and density matrix treatments. iii) Evaluation of the importance of entropic effects and quantum tunneling in enzyme catalysis and incorporation of calculated isotope effects in the interpretation of enzymatic reaction mechanisms. iv) Examination of the validity of linear free energy relationships in enzymes. v) Studies of electrostatic effects in macromolecules.